function [J grad] = nnCostFunction(nn_params, ...
                                   input_layer_size, ...
                                   hidden_layer_size, ...
                                   num_labels, ...
                                   X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
%   X, y, lambda) computes the cost and gradient of the neural network. The
%   parameters for the neural network are "unrolled" into the vector
%   nn_params and need to be converted back into the weight matrices. 
% 
%   The returned parameter grad should be a "unrolled" vector of the
%   partial derivatives of the neural network.
%

% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
                 hidden_layer_size, (input_layer_size + 1));

Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
                 num_labels, (hidden_layer_size + 1));

% Setup some useful variables
m = size(X, 1);
         
% You need to return the following variables correctly 
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));

% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
%               following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
%         variable J. After implementing Part 1, you can verify that your
%         cost function computation is correct by verifying the cost
%         computed in ex4.m
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
%         Theta2_grad, respectively. After implementing Part 2, you can check
%         that your implementation is correct by running checkNNGradients
%
%         Note: The vector y passed into the function is a vector of labels
%               containing values from 1..K. You need to map this vector into a 
%               binary vector of 1's and 0's to be used with the neural network
%               cost function.
%
%         Hint: We recommend implementing backpropagation using a for-loop
%               over the training examples if you are implementing it for the 
%               first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
%         Hint: You can implement this around the code for
%               backpropagation. That is, you can compute the gradients for
%               the regularization separately and then add them to Theta1_grad
%               and Theta2_grad from Part 2.
%
h1 = sigmoid([ones(m, 1) X] * Theta1');
h2 = sigmoid([ones(m, 1) h1] * Theta2');

for i=1:m
    yy = (y(i) == [1:num_labels]');
    J = J-(yy'*log(h2(i,:)')+(1-yy)'*log(1-h2(i,:))');
end

J = J/m;

theta1_reg = 0;

for i=1:hidden_layer_size
    theta1_reg = theta1_reg + Theta1(i,2:size(Theta1,2))*Theta1(i,2:size(Theta1,2))';
end

theta2_reg = 0

for i=1:num_labels
    theta2_reg = theta2_reg + Theta2(i,2:size(Theta2,2))*Theta2(i,2:size(Theta2,2))';
end

J = J+ lambda/(2*m) *(theta1_reg+theta2_reg);

Delta2 = zeros(num_labels,hidden_layer_size+1);
Delta1 = zeros(hidden_layer_size,input_layer_size+1);


for t=1:m
   yy = (y(t) == [1:num_labels]');
   z_2 = Theta1*[1 X(t,:)]';
   a_2 = sigmoid(z_2);
   z_3 = Theta2*[1;a_2];
   a_3 = sigmoid(z_3);
   
   delta3 = (a_3  - yy);
   
   delta2 = (Theta2(:,2:end)'*delta3) .* sigmoidGradient(z_2);
   
   Delta2 =Delta2+ delta3*[1;a_2]';
   Delta1 =Delta1+ delta2*[1 X(t,:)];
    
    
end



Theta1_grad(:,1) = 1/m * Delta1(:,1);
Theta1_grad(:,2:end) = (1/m) * Delta1(:,2:end) + (lambda/m)*Theta1(:,2:end) ;

Theta2_grad(:,1) = 1/m * Delta2(:,1);
Theta2_grad(:,2:end) = (1/m) * Delta2(:,2:end) +  (lambda/m)*Theta2(:,2:end);


% -------------------------------------------------------------

% =========================================================================

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];


end
